Question

Sum of the reciprocals of man's age(in years) 5years ago and 4 years from now is 29/190. Find s present age.

Answer 1

Answer:

Let the man's age be A

His age 5 years ago will be A - 5

His age 4 years from now will be A + 4

[ 1 / (A - 5) ] + [ 1 / (A + 4) ] = 29 / 190

[ (A + 4) + (A - 5) ] / [ (A - 5)x(A + 4) ] = 29 / 190

(2A - 1) / (A² + 4A - 5A - 20) = 29 / 190

190 x (2A - 1) = 29 x (A² + 4A - 5A - 20)

380A - 190 = 29 x (A² - A - 20)

380A - 190 = 29A² - 29A - 580

380A + 29A - 190 + 580 = 29A²

409A + 390 = 29A²

29A² - 409A - 390 = 0

By solving equation ,

A = 15 years

Answer 2

Step-by-step explanation:

Given Sum of the reciprocals of man's age(in years) 5 years ago and 4 years from now is 29/190 .  Find his present age.

• Let the man’s age be x
• According to the question his age 5 years ago will be x – 5
• Also his age 4 years from now will be x + 4
• Now 1/x – 5 + 1 / x + 4 = 29 / 190
• So x + 4 + x – 5 / (x – 5) (x + 4) = 29 / 190
• 2 x – 1 / x^2 – 5x + 4x – 20 = 29 / 190
• 2x – 1 / x^2 – x – 20 = 29 / 190
• 380 x – 190 = 29 x^2 – 29 x – 580
• 380 x + 29 x – 29 x^2 – 190 + 580 = 0
• 29 x^2 – 409 x – 390 = 0
• Now x = - b ± √b^2 – 4ac / 2a
•    So x = - (- 409) ± √(409)^2 – 4(29)(- 390) / 2 (29)
•    So x = 409 ± √212521 / 58
•   Or x = 409 + 461 / 58
•  Or x = 870 / 58
•  Or x = 15 years.
• So his present age is 15 years.

Reference link will be

https://brainly.in/question/3133434